The present invention relates in general to integrated filters, and in particular to high frequency transconductor-capacitor (g.sub.m -C) integrated filters.
A transconductor is an element that delivers an output current proportional to the input signal voltage: i=g.sub.m *Vin, where g.sub.m is the transconductance of the element. When a capacitor is connected to the output of a transconductor, an integrator is obtained: Vo/Vin=g.sub.m *(1/sC). Monolithic filters may thus be implemented using the g.sub.m -C integrator.
In high-frequency g.sub.m -C filters the most important building block is the transconductor element. Various circuit implementations of the transconductor element have been proposed to optimize various aspects of its performance characteristics including linearity, speed, and input dynamic range. The bipolar transistor, for example, has higher transconductance than that of metal-oxide-semiconductor (MOS) transistor and therefore exhibits higher bandwidth. However, bipolar transistor-based transconductors have limited input dynamic range. The MOS transconductor on the other hand enjoys a larger input linear range, but it also suffers from a limited input dynamic range.
FIG. 1 shows a pair of MOS inverters that when biased in the saturation region implement a differential transconductor. This transconductor uses the quadratic relation between the drain current and the gate-to-source voltage of an MOS transistor to realize linear performance. The drain currents of an n-channel and a p-channel MOS transistor in saturation are given by: EQU i.sub.dn =(.mu..sub.0 C.sub.ox /2)(W.sub.n /L.sub.n)(v.sub.gsn -v.sub.tn).sup.2 =(.beta..sub.n /2)(v.sub.gsn -v.sub.tn).sup.2 EQU i.sub.dp =(.mu..sub.0 C.sub.ox /2)(W.sub.p /L.sub.p)(v.sub.gsp -v.sub.tp).sup.2 =(.beta..sub.p /2)(v.sub.gsp -v.sub.tp).sup.2
Thus, the differential output current in terms of the differential input voltage is: EQU i.sub.out =v.sub.i (v.sub.cc -v.sub.tn +v.sub.tp).sqroot..beta..sub.n .beta..sub.p
This yields a perfect linear relation between the input voltage, Vi=Vip-Vin, and the output current i.sub.out. The inverter-based transconductor has a perfect linearity performance if other secondary effects are neglected. One drawback of this transconductor is that the frequency tuning of the filter must be performed by changing the supply voltage V.sub.cc. This requires a voltage regulator and associated compensation network, which increases the minimum power supply voltage and limits the frequency response of the filter.
FIG. 2 shows a schematic of a current controlled differential transconductor. The major difference between this circuit and the inverter based transconductor of FIG. 1 is that two current sources are used here to bias the transconductor so that the corner frequency can be controlled by current rather than the supply voltage. Transistors M2 and M3 have been added to minimize the common-mode and maximize the differential-mode output impedance. This implementation eliminates the required supply voltage control circuitry and the associated compensation network. The performance of this transconductor is, however, highly dependent on the output impedance of transistors M1, M2, and M3. The transfer function of an ideal integrator (with infinite output impedance) has a pole at zero frequency which introduces a -90 degrees phase shift. The effect of finite output impedance is to move the pole from zero to a finite frequency, causing an undesired phase shift in the frequency response of the integrator. Thus, it is critical to maximize the differential output impedance of the transconductor.
The differential output impedance of the transconductor of FIG. 2 is given by: EQU R.sub.out =[1/(g.sub.m2 +.SIGMA.g.sub.ds1,2,3 -g.sub.m3)]
where, g.sub.m2 and g.sub.m3 are the transconductances of MOS transistors M2 and M3, and the term .SIGMA.g.sub.ds1, 2, 3 represents the sum of output conductances (g.sub.ds) for transistors M1, M2, and M3. Therefore, to obtain infinite differential output impedance for the integrator, the sizes of transistors M1, M2, and M3 should be scaled such that the terms in the denominator of the R.sub.out equation cancel out. While an approximate cancellation may be achieved to a first degree, the performance of the integrator suffers from secondary effects. For example, the output conductance g.sub.ds of an MOS transistor does not track gm as the bias current varies. There may be as much as 2% to 5% variation in the ratio of gm/g.sub.ds at different current levels. Also, the g.sub.ds of an MOS transistor does not track g.sub.m over temperature and process variations. Thus, the performance of an integrator based on the transconductor element of FIG. 2 is adversely affected by a finite and variable transistor output impedances.
A conventional approach to increasing the differential output impedance of the transconductor of FIG. 2 is to add a second level of transistors (M1', M2', and M3') in a cascode connection. While the cascode transistors exhibit higher output impedance, the structure adds an extra node (cascode node) in the signal path which causes undesirable high frequency phase shift.
There is therefore a need for an improved transconductor circuit for high frequency filtering applications.